A.V. van den Berg

Human gaze stability in the horizontal, vertical and torsional direction during voluntary head movements, evaluated with a three-dimensional scleral induction coil technique

The stability of gaze in three dimensions (horizontal, vertical and torsion) was measured with a new type of scleral search coil in eight emmetropic observers. Subjects held the head still or oscillated it at 0.16-0.67 Hz (amplitude about 10 deg) in the horizontal, vertical or torsional plane while fixating a point target at optical infinity. Veridical gaze and head coordinates were calculated with full correction for non-linear goniometric relations and for cross-coupling artifacts due to misalignments of the coil on the eye. The amount of gaze instability in the horizontal and vertical direction was virtually identical. With the head still, in either of these directions the mean standard deviation of gaze position (inclusive saccades) was about 7 min arc; mean non-saccadic retinal image speeds were 20-30 min arc/sec. During head oscillation these values increased to about 16 min arc and 1 deg/sec; a mean of about 2.5% of the head motion remained uncorrected by the compensatory eye movements. These findings agree well with our earlier results for the horizontal plane; the effect of the corrections was relatively small because the adventitious cross-coupling of horizontal and vertical to torsional head movements proved to be usually smaller than 10%. However, the corrections were important when head torsion was deliberately produced. Gaze stability in the torsional plane was considerably inferior to that in the horizontal and vertical plane. With the head held still, the mean SD of torsional gaze position was about 17 min arc; mean torsional non-saccadic retinal image speed was about 46 min arc/sec. Gain of the torsional compensatory eye movements was frequency dependent and rose from about 0.26 in static conditions (0 Hz) to about 0.42 at 0.16 Hz and 0.64 at 0.67 Hz. Accordingly, position instability and speed of the retinal image in torsion were about an order of magnitude larger than in the horizontal and vertical direction.

Binocular eye orientation during fixations: Listing's law extended to include eye vergence

Abstract Any eye position can be reached from a position called the primary position by rotation about a single axis. Listings law states that for targets at optical infinity all rotation axes form a plane; the so-called Listing plane. Listings law is not valid for fixation of nearby targets. To document these deviations of Listings law we studied binocular eye positions during fixations of point targets in the dark. We tested both symmetric (targets in a sagittal plane) and asymmetric vergence conditions. For upward fixation both eyes showed intorsion relative to the position that would have been taken if each eye followed Listings law. For downward fixation we found extorsion. The in- or extorsion increased approximately linearly with the vergence angle. The direction of the Listing axis and the turn angle about this axis can be described by rotation vectors. Our observations indicate that for fixation of nearby targets the rotation vectors of the two eyes become different and are no longer located in a single plane. However, we find that it is possible to decompose the rotation vector of each eye into the sum of a symmetric and an anti-symmetric part, each with its own properties. (1) The symmetric part is associated with eye version. This component of the rotation vector is identical for both eyes and lies in Listings plane. In contrast to the classical form of Listings law, this part of the rotation vector lies in Listings plane irrespective of the fixation distance. (2) The anti-symmetric part of the rotation vector is related to eye vergence. This component is of equal magnitude but oppositely directed in each eye. The anti-symmetric part lies in the mid-sagittal plane, also irrespective of fixation distance. For fixation of targets at optical infinity the anti-symmetric part equals zero and the eye positions obey the classical form of Listings law. Thus, the symmetric and anti-symmetric parts of the rotation vectors are restricted to two perpendicular planes. Combining these restrictions in a model, with the additional restriction that the vertical vergence equals zero during fixation of point targets, we arrive at the prediction that the cyclovergence is proportional to the product of elevation and horizontal vergence angles. This was well born out by the data. The model allows to describe the binocular eye position for fixation of any target position in terms of the bipolar coordinates of the target only (i.e. using only three degrees of freedom instead of the six needed for two eyes).

Robustness of perception of heading from optic flow.

Heading discrimination in optic flow stimuli was investigated in 5 humans. Flow patterns consisted of a computer generated motion sequence which showed a mixture of randomly moving and coherently-moving points. The motion of the coherently-moving fiducial points was completely determined by the changing position of the observers simulated vantage point. Ego-rotation as well as ego-translation was simulated. Noise and fiducial points were confined to the ground plane in most experiments. In one experiment the points formed a cloud with no visible horizon. The results indicate that heading perception is robust against degradation of the flow-field by the presence of noise or by the reduction of the lifetime of the fiducial points. The results suggest that points, which move independently from the reference frame as formed by the fiducial points, are to a large extent removed from the analysis of optic flow by the visual process which derives the heading. The motion of recognizable points at infinity (like the horizon) appears to be essential for robust heading perception in the presence of ego-rotations.

A direct test of Listing's law—I. Human ocular torsion measured in static tertiary positions

The validity of Listings law was reinvestigated by means of a direct test. Horizontal, vertical and torsional eye movements were measured simultaneously with a recently developed scleral induction coil. Either eye of 4 subjects was measured monocularly. Eye position were measured in Fick coordinates and ocular torsion values were compared to the theoretical ones predicted by Listings law. During consecutive measurements in the primary position torsion values were close to zero although considerable fluctuations of torsion were seen. Torsion values in the secondary positions were also close to zero. In the tertiary positions torsion in the direction as predicted by Listings law and increasing with eccentricity was recorded. In the temporal quadrants mean torsion was quantitatively in agreement with Listings law; torsion values in the nasal quadrants however showed systematically larger values and this discrepancy increased with eccentricity to more than 50%. Statistical support for this finding however, was seen only in 4 out of 8 eyes. Symmetry could be obtained by shifting the chosen horizontal primary position (gaze parallel to the midplane) in the temporal direction; as a consequence all measured torsion values would exceed the ones specified by Listings law. Torsion values varied idiosyncratically among subjects and among the left and right eyes of any one subject. It is concluded that Listings law specifies ocular torsion only approximately: physiological eye movements show considerable stochastical as well as systematical deviations from this law.

A direct test of Listing's law--II. Human ocular torsion measured under dynamic conditions.

Ocular torsion was recorded with a scleral search coil technique in five normal subjects. The dynamic aspects of torsion were investigated during monocular fixation, blinking, smooth pursuit and saccades. Torsion near the primary position showed considerable short-term (SD about 0.25 deg) and a much larger long-term fluctuation (SD about 2.3 deg). During saccades between diagonally opposite tertiary positions torsion transiently reached values approximating those in the sustained primary position. During smooth pursuit across the primary position, the minimal values of torsion varied with the direction and the trajectory of pursuit, in violation of Donders law. Changes in torsion associated with horizontal and vertical saccades and during the aftermath of blinks often had a sluggish, exponential time course. During eye movements around a circular or square trajectory torsion showed hysteresis. During clockwise pursuit the right eye showed relative intorsion compared to counterclockwise pursuit. It is proposed that central nervous control of torsion is usually imprecise, and that the eye follows Listings and Donders laws only approximately.

Humans combine the optic flow with static depth cues for robust perception of heading

The retinal flow during normal locomotion contains components due to rotation and translation of the observer. The translatory part of the flow-pattern is informative of heading, because it radiates outward from the direction of heading. However, it is not directly accessible from the retinal flow. Nevertheless, humans can perceive their direction of heading from the compound retinal flow without need for extra-retinal signals that indicate the rotation. Two classes of models have been proposed to explain the visual decomposition of the retinal flow into its constituent parts. One type relies on local operations to remove the rotational part of the flow field. The other type explicitly determines the direction and magnitude of the rotation from the global retinal flow, for subsequent removal. According to the former model, nearby points are most reliable for estimating ones heading. In the latter type of model the quality of the heading estimate depends on the accuracy with which the ego-rotation is determined and is therefore most reliable when based on the most distant points. We report that subjects underestimate the eccentricity of heading, relative to the fixated point in the ground plane, when the visible range of the ground plane is reduced. Moreover we find that in perception of heading, humans can tolerate more noise than the optimal observer (in the least squares sense) would do if only using optic flow. The latter finding argues against both schemes because ultimately both classes of model are limited in their noise tolerance to that of the optimal observer, which uses all information available in the optic flow. Apparently humans use more information than is present in the optic flow. Both aspects of human performance are consistent with the use of static depth information in addition to the optic flow to select the most distant points. Processing of the flow of these selected points provides the most reliable estimate of the ego-rotation. Subsequent estimates of the heading direction, obtained from the translatory component of the flow, are robust with respect to noise. In such a scheme heading estimates are subject to systematic errors, similar to those reported, if the most distant points are not much further away than the fixation point, because the ego-rotation is underestimated.

Directional asymmetries of human optokinetic nystagmus

SummaryOptokinetic nystagmus in the four principal directions was investigated on the occurrence of directional asymmetries in 7 normal human subjects. Instructions were aimed at obtaining a ‘stare’ type of OKN. The movement of both eyes was recorded simultaneously with a scleral sensor-coil method. Subjects viewed a full-field random dot pattern rotating at velocities of 9 to 57 deg/s binocularly, as well as monocularly with either eye. Gain was always less than 0.85 and decreased when the pattern velocity increased. Horizontal and vertical nystagmus differed in a number of respects. (1) We found no evidence for an overall asymmetry for rightward or leftward, motion. However, human OKN showed a clear preference for upward stimulus motion. Mean gain was ca. 0.15 larger for upward than for downward motion. (2) The decrease of the gain of OKN as a function of increasing stimulus velocity was steeper for vertical than for the horizontal direction. (3) The eyes moved nearly perfectly yoked for vertical pattern movement, irrespective of the viewing conditions. In contrast, during horizontal OKN the gain of the eye tracking in the nasal direction was higher (by about 4%) than the gain of the other eye moving simultaneously in the temporal direction. This difference persisted irrespective of the viewing conditions and appears to be motor, not sensory in origin. In addition, for any direction of the pattern motion a statistically significant increase of the gain occurred when the pattern motion was seen binocularly instead of monocularly with either eye.

Judgements of heading

Abstract To study the contribution of vision to the perception of ego-motion, one often dissociates the retinal flow from the corresponding extra-retinal information on eye, head and body movement. This puts the observer in a conflict concerning the experienced ego-motion. When the retinal flow of a translating and rotating eye is shown to a stationary eye, observers often perceive ego-motion on a curved path. In contrast, when they receive the same retinal flow with a rotating eye subjects correctly perceive the simulated rectilinear ego-motion. Thus, different visual representations of ego-motion gain precedence when using the conflict stimulus and when using conditions in which the visual and extra-retinal information accord. Because the flow-pattern can be decomposed in many different ways, the brain could represent the same flow-pattern as a rotation about an axis through the eye plus rectilinear ego-motion or a rotation about an axis outside the eye (corresponding to circular ego-motion) plus motion towards the axis of rotation. The circular motion path percept minimizes the conflict with extra-retinal eye movement information if the axis of rotation is placed at the fixation point. However, in simulated eye rotation displays subjects also perceive illusory motion in depth of the stationary fixation point. This illusory motion is argued to reflect the ego-centric decomposition. Errors are small when subjects judge their heading on the basis of this illusory motion. For the same displays much larger errors are made, however, when subjects judge heading from the entire motion pattern, which often results in perceived ego-motion on a curved path. This indicates that subjects can choose between two different representations of ego-motion resulting in different perceived heading. Copyright

Human smooth pursuit during transient perturbations of predictable and unpredictable target movement.

SummaryThe predictive component of human smooth pursuit was studied by perturbing sinusoidal target motion at unpredictable instants. The disturbances consisted of either a brief period of stabilization of the target on the fovea or a replacement of the sine by a ramp displacement for half a period. To minimize the effects of a possible change of the tracking strategy by the subject the transitions were masked and only the initial part of the response to the disturbance was analyzed. After stabilization on the fovea the eye oscillation continued at the frequency of the preceding target movement for about one half-cycle, whereupon the oscillation was rapidly damped. The mean unidirectional smooth eye acceleration was 70% of the mean unidirectional target acceleration prior to the stabilization. This suggests that during pursuit of a sinusoidal target movement about 75% of the oculomotor response is generated by predictive processes. When the sine was replaced by a ramp, starting at the velocity zero-crossing, the eye accelerated away from the target for ca. 180 ms irrespective of the frequency of prior tracking. In contrast, when the ramp started at the peak velocity of the sinusoidal target motion the eye accelerated away from the target for more than a quarter period. After foveal stabilization during pursuit of a pseudorandom stimulus, the eye continued to oscillate for less than one period at approximately the highest frequency present in the stimulus. The frequency characteristics of human smooth pursuit of predictable as well as unpredictable target motion were correctly simulated by a model, which derived its predictive properties from a lead element, tuned to the current frequency of the target motion.

Smooth eye movements and spatial localisation

We asked subjects to align a target that flashed as their eyes rotated to the right in pursuit of a moving ring, with a target that flashed as their eyes rotated to the left in pursuit of the ring. Subjects systematically mislocalised the targets in the direction of pursuit. When the ring and flashes were the only structures that were visible, the alignment error was about 4 cm, corresponding to a timing error of about 100 ms. The timing error was independent of the position along the rings path, but did depend to some extent on pursuit velocity. Adding a textured background reduced the mislocalisation considerably, presumably because it enabled subjects to localise the targets relative to the surrounding. There was almost no mislocalisation if the subject was not pursuing the ring. It is suggested that the mislocalisation arises because incoming retinal signals are combined directly with outgoing oculo-motor commands, with no attempt to account for any of the involved neuronal and muscular delays.